2018/06/06 by Patrice Bertail, Bertail, Patrice, François Portier +1 · 2 citations
Computer Science · Mathematics · #Complexity and Algorithms in Graphs #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Graph Theory and Algorithms #Markov Chains and Monte Carlo Methods #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1806.02107
openalex publication_date 2018/06/06 · openalex created_date 2018/06/13 · openalex updated_date 2026/07/28
Following the seminal approach by Talagrand, the concept of Rademacher complexity for independent sequences of random variables is extended to Markov chains. The proposed notion of "block Rademacher complexity" (of a class of functions) follows from renewal theory and allows to control the expected values of suprema (over the class of functions) of empirical processes based on Harris Markov chains as well as the excess probability. For classes of Vapnik-Chervonenkis type, bounds on the "block Rademacher complexity" are established. These bounds depend essentially on the sample size and the probability tails of the regeneration times. The proposed approach is employed to obtain convergence rates for the kernel density estimator of the stationary measure and to derive concentration inequalities for the Metropolis-Hasting algorithm.